Hybrid quantum circuits improve high dimensional data regression and reconstruction
Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction
Machine Learning
Summary
Many tasks like predicting multiple outputs at once or reconstructing images from data require handling complex, high-dimensional information. The paper proposes a new kind of hybrid quantum circuit that combines quantum processing with a classical step right after measurement, allowing it to predict many values at once efficiently. The researchers show that simple quantum circuits can approximate important functions and, when tested on synthetic images and a known benchmark, their hybrid approach performs as well as advanced classical methods. They also find both the quantum and classical parts are necessary for the best results.
What this means in practice
- •For machine learning engineers: Enable efficient multivariate regression models on high-dimensional datasets using hybrid quantum circuits combined with classical post-processing.
- •For image processing teams: Use hybrid quantum-classical models to reconstruct synthetic or real images with accuracy comparable to established classical methods.
Authors
Koffi Ognandon Ayena, Frédéric Holweck, Serge Iovleff, Amah S d'Almeida
Abstract
Variational quantum circuits (VQCs) are parameterized quantum circuits optimized classically. We propose a hybrid variational quantum circuit (HVQC) extending VQCs with a classical affine post-measurement layer, enabling vector-valued regression without the linear overhead of independent scalar circuits. Theoretically, we show that elementary one-and two-qubit circuits can approximate quadratic functions and products via data re-uploading and entanglement, providing the foundations of the full architecture. Experimentally, on two synthetic image reconstruction datasets and the Friedman1 benchmark (40,568 test samples), our HVQC matches Gaussian Process Regression and outperforms XGBoost and Random Forest. An ablation study confirms that both quantum and classical components are essential, and results highlight the central role of the feature map in hybrid quantum-classical models.